In an open organ pipe ν₃ and ν₆ are 3rd and 6th harmonic frequencies, respectively. If ν₆ - ν₃ = 2200 Hz then length of the pipe i $s ______$ mm.
(Take velocity of sound in air is 330 m/s.)

Question

In an open organ pipe ν₃ and ν₆ are 3rd and 6th harmonic frequencies, respectively. If ν₆ - ν₃ = 2200 Hz then length of the pipe i s ______ mm. (Take velocity of sound in air is 330 m/s.)

G1 Physics · Accepted Answer

For an open organ pipe, νₙ = nv/(2L). Therefore, ν₆ - ν₃ = 6v/(2L) - 3v/(2L) = 3v/(2L). Given, ν₆ - ν₃ = 2200 Hz, v = 330 m/s. Hence, 3×330/(2L) = 2200. Therefore, L = 3×330/(2×2200) = 0.225 m = 225 mm. Correct option: B.